Question

the area of equilateral triangle is 100√3cm². find the perimeter of the triangle

Answer 1

let side of equilateral ∆=x
area of equilateral ∆=√3/4×side ^2
100√3=√3/4×x^2
100×4=x^2
400=x^2
so, x=20cm
perimeter of equilateral ∆= 3×side=3×x
=3×20=60cm

Answer 2

✬ Perimeter = 60 cm ✬

Step-by-step explanation:

Given:

• Area of equilateral triangle is 100√3 cm².

To Find:

• What is the perimeter of the triangle ?

Solution: We know that the formula for area of equilateral triangle is

★Area of Equilateral triangle=√3(a)²/4★

A/q

Putting the values on formula

$\implies{\rm }$ 100√3 = √3(a)²/4

$\implies{\rm }$ 100√3 $\times$ 4 = √3(a)²

$\implies{\rm }$ 400√3 = √3(a)²

$\implies{\rm }$ 400√3/√3 = a²

$\implies{\rm }$ 400 = a²

$\implies{\rm }$ √400 = a

$\implies{\rm }$ √20 $\times$ 20 = a

$\implies{\rm }$ 20 cm = a

Hence, The measure of wach side of triangle is 20 cm.

Since, All the three sides of an equilateral triangle are equal. Therefore its perimeter

★ Perimeter = 3 $\times$ Side ★

➟ 3 $\times$ 20

➟ 60 cm

Hence, the perimeter of equilateral triangle is 60 cm.